Since the pioneering work of Yablonovitch in the late 1980s, photonic band gap (PBG) structures have emerged as a growth area for research and development. The existence of local and global photonic band gaps in periodic dielectric and/or metallic structures has enabled physicists and engineers to find novel areas of applications. Previously proposed or demonstrated applications of dielectric PBG structures range from the controlling of spontaneous emission in optical devices, to the applications of photonic crystals in semiconductor lasers and photovoltaic cells, to the omniguide formed with alternating dielectric layers. While initial studies of PBG structures were primarily focused on dielectric PBG structures, metallic PBG structures, as well as dielectric-metallic hybrids, have received considerable attention recently, because of their applications in rf accelerators and high-power microwave vacuum electron devices, and in the transmission and filtering of microwaves. In particular, single-mode PBG rf accelerating cells have been demonstrated by creating a single defect in PBG lattices, and a PBG resonator gyrotron has been demonstrated experimentally with high mode selectivity.
There are two important aspects that need to be studied in order to facilitate the design of metallic PBG devices. One involves the wave propagation in the bulk of the metallic PBG structure, and the other concerns the wave interaction with the interface between the metallic PBG structure and vacuum, e.g., mode confinement in a metallic PBG cavity. For analyses of metallic PBG cavities formed by single or multiple defects in the PBG structure, finite-element codes such as SUPERFISH and HFSS are ideally suited. The SUPERFISH eigenmode solver was written at the Los Alamos National Laboratory (LANL), and is available at no cost from the web site http://laacg1.lanl.gov/laacg/services/psugall.html. Ansoft High Frequency Structure Simulator (HFSS) is a commercially-available 3D electromagnetic code. For studies of wave propagation in the bulk of metallic PBG structures, on the other hand, the generalized Rayleigh expansion method, plane-wave expansion method, and finite-difference time-domain scheme have been used.
One of the most important and computationally challenging problems is the calculation of the global photonic band gaps in metallic lattices. While a number of papers have dealt with the global photonic band gaps in dielectric lattices, results for a metallic lattice have only been obtained for TM modes in the lowest gap of a square lattice.